A section for the map \(\pi : G\rightarrow G/H\)  is just a map \(\varphi : G/H \rightarrow G\)  such that \(\varphi (gH)\in gH\) , since we point out the trivial identity \(\pi ^{-1}(gH)=gH\) . To have the notion of intrinsic Lipschitz section we need the group \(G\)  to be equipped with a distance which we assume left-invariant. We refer to such a \(G\)  as a metric group. The reader can see [1]}.
